The present invention relates to a method for forming a pattern by electron-beam lithography.
In electron-beam lithography, an electron beam is irradiated at a high velocity onto a resist film, which is formed on a substrate and is highly sensitive to the electron beam, thereby writing or transferring a desired pattern onto the resist film.
According to electron-beam lithography, a pattern with a line width of 0.1 .mu.m or less can be written at a high resolution, and a plurality of patterns can be aligned with, and overlaid on, each other very accurately. Thus, electron-beam lithography has been applied to various sorts of fine-line processing to form patterns for a photomask, interconnection for a semiconductor device, and so on.
During an electron-beam lithography process, electrons, which have impinged onto a resist film formed on a substrate, collide against numerous atoms with a smaller atomic weight (e.g., carbon atoms) making up the resist film to scatter forward. In addition, after the electrons have passed through the resist film and entered the substrate, the electrons also collide against numerous atoms with a larger atomic weight (e.g., silicon atoms) making up the substrate to scatter backward. As a result, so-called "proximity effects" are caused. Specifically, not only a target region of the resist film, on which the electron beam should be incident, but also surrounding regions thereof are unintentionally exposed due to the electrons that have scattered forward and/or backward, thus degrading the resulting pattern accuracy.
Thus, to improve the resultant pattern accuracy in the electron-beam lithography, proximity effect correction is indispensable. That is to say, before a resist film is irradiated with an electron beam, the exposure dose of the electron beam should be controlled in view of the proximity effects.
Hereinafter, the forward and backward scattering of electrons and a conventional method for compensating for the proximity effects as disclosed in J. Appl. Phys., Vol. 50, No. 6, June 1979, pp. 4371-4387 will be described with reference to FIGS. 5(a) and 5(b).
FIG. 5(a) illustrates an exemplary trajectory of an electron 3, which scatters forward within a resist film 2 and then backward within a substrate 1.
As shown in FIG. 5(a), first, the electron 3 scatters forward within the resist film 2 as indicated by a portion 4 of the trajectory (the lateral range 6 of which is defined from the point where the electron 3 enters the resist film 2). Then, the electron 3 scatters backward within the substrate 1 as indicated by another portion 5 of the trajectory (the lateral range 7 of which is also defined from the point where the electron 3 enters the resist film 2).
FIG. 5(b) illustrates Gaussian distributions representing exemplary distributions of the lateral ranges 6 and 7 of the electron 3 scattering forward and backward, respectively.
As shown in FIG. 5(b), the distribution of the lateral range 6 of the forward-scattered electron is represented as a first Gaussian distribution 8 with a standard deviation .beta..sub.f (which will herein be called a "forward-scattering radius"), while the distribution of the lateral range 7 of the backscattered electron is represented as a second Gaussian distribution 9 with a standard deviation .beta..sub.b (which will herein be called a "backscattering radius"). Also, the lateral range 7 of the backscattered electron is defined by a maximum radius r.sub.b that the backscattered electron can possibly reach (in this specification, this radius will be called a "maximum radius r.sub.b of backscattered electron's reach"). In other words, the backscattered electron never goes beyond the limit defined by the maximum radius r.sub.b, which is the longest distance as measured from the point where the electron 3 enters the resist film 2.
The forward-scattering radius .beta..sub.f, backscattering radius .beta..sub.b and maximum radius r.sub.b differ depending on the accelerating voltage of an electron beam and the materials compositions of a substrate and a resist film. In an ordinary situation, where a silicon substrate and a resist film with a carbon skeleton are used and the resist film is irradiated with an electron beam at an accelerating voltage of 70 keV, the forward-scattering radius .beta..sub.f, backscattering radius .beta..sub.b and maximum radius r.sub.b are about 0.05 .mu.m, about 20 .mu.m and about 35 .mu.m, respectively.
When a resist film is irradiated with an electron beam, the respective energies of the forward- and backward-scattered electrons are absorbed into the resist film. Thus, the intensity distribution of energy deposited in the resist film about the center of the electron beam focused is the sum of first and second intensity distributions of energy deposited in the resist film by the forward- and backward-scattered electrons, respectively, around the center.
The first intensity distribution of energy deposited by the forward-scattered electron can be represented as the distribution of the lateral range of the forward-scattered electron and approximated to the first Gaussian distribution 8 with a standard deviation equal to the forward-scattering radius .beta..sub.f (see FIG. 5(b)). On the other hand, the second intensity distribution of energy deposited by the backscattered electron can be represented as the distribution of the lateral range of the backscattered electron and approximated to the second Gaussian distribution 9 with a standard deviation equal to the backscattering radius .beta..sub.b (see also FIG. 5(b)).
The intensity of energy deposited by the forward-scattered electron at the center of the electron beam focused on the resist film is several hundred times as high as that of energy deposited by the backscattered electron at the center of the electron beam focused on the resist film.
A conventional method for correcting the proximity effects includes the following process steps. First, the forward-scattering radius .beta..sub.f, backscattering radius .beta..sub.b and first and second intensity distributions of energy deposited by the forward- and backward-scattered electrons are derived based on experiments, simulations or the like. Next, the first and second intensity distributions are approximated to the Gaussian distributions with the standard deviations equal to the forward-scattering radius .beta..sub.f and backscattering radius .beta..sub.b, respectively. Subsequently, a function representing a sum of the first and second intensity distributions approximated and a function representing a predetermined exposure dose at an arbitrary position in the resist film (i.e., a function representing an exposure pattern) are convoluted to calculate total energy deposited at that arbitrary position. Then, the function representing an exposure pattern is modified so as to equalize the total energy deposited with a predetermined value. According to the conventional method, after the exposure dose of the electron beam has been controlled by this proximity effect correction technique, the resist film is irradiated with the electron beam at the controlled dose, thereby writing a desired pattern onto the resist film. Finally, the resist film, which has been irradiated with the electron beam, is developed, thereby selectively removing unnecessary portions of the resist film and defining a resist pattern.
To improve the accuracy of proximity effect correction, an intensity distribution of energy deposited by a secondary electron, which has been formed by the collision of the incoming electron against the atoms making up the substrate, is sometimes used. However, the secondary electron move at a relatively low velocity and the lateral range of the secondary electron is about several hundredths of the backscattering radius .beta..sub.b. Thus, the accuracy of proximity effect correction cannot be greatly improved even by the use of the intensity distribution of energy deposited by the secondary electron.
Also, according to the majority of previous methods for compensating for the proximity effects, the convolution is employed just for the purpose of high-speed approximation. Furthermore, these methods suppose that the resist film is always exposed due to the forward- and backward-scattered electrons.
The conventional electron-beam lithography utilizing the proximity effect correction technique has been adopted where the accelerating voltage of the electron beam is less than 50 keV. In order to increase the resolution at the electron-beam lithography, however, the accelerating voltage of the electron beam should be 50 keV or more.
Nevertheless, in accordance with the conventional electron-beam lithography utilizing the proximity effect correction technique, if the accelerating voltage of the electron beam is defined at 50 keV or more, the accuracy of proximity effect correction declines with the increase in accelerating voltage. Thus, the resultant pattern accuracy also declines accordingly.